The check in the back should not be an issue. Warm the stave thoroughly then let thin super glue soak down into it. Capillary action combined with the warmth thinned glue will suck the glue down to the bottom of the check.
Similar remedy on the one in the fade/handle. More than likely, based solely upon what I can see and surmise, it will not be an issue. But to be honest I can't really "see" the feature in proper context from the pics. Sometimes here's not substitute for actually being able to handle the stave oneself.
Most osage bows can be 3/4" (wide) x 1 1/2" (deep) at the arrow pass with no problem. I like at least 5/8" in the fade but you can get away with a lot here too, including a little bit of movement. Also bear in mind with decent osage 1 1/2" of width will make darn near as much bow as you please, 60#+ anyway. And one need not necessarily achieve that max width abruptly, rather as far out at 6", 7" beyond the arrow pass depending upon the overall design and tiller. So, if you can envision, the width profile could be 3/4" at the arrow pass straight taper to 1 1/2" (or less) at 7" out into the limbs.
I'd base my choice about chasing another ring on other potential issues, like what this ring looks like versus the next, the whole bow taken into account, etc.
Sorry if I'm volunteering too much. Haven't read the whole thread, and you may be more experienced than I give credit.